Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 5, −1, −7, −13, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 11
- d = −1 − 5 = −6
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −6 = −6n + 11
2.Find the 9th term of the arithmetic sequence 4, 7, 10, 13, …
Answer: 28
- a = 4, d = 3
- T9 = 4 + 8 × 3 = 28
3.For the arithmetic sequence 18, 22, 26, 30, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 14
- d = 22 − 18 = 4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 4 = 4n + 14
4.Find the 8th term of the arithmetic sequence 5, 1, −3, −7, …
Answer: −23
- a = 5, d = −4
- T8 = 5 + 7 × −4 = −23
5.Find the 10th term of the arithmetic sequence 1, 4, 7, 10, …
Answer: 28
- a = 1, d = 3
- T10 = 1 + 9 × 3 = 28
6.For the arithmetic sequence −8, 0, 8, 16, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 16
- d = 0 − (−8) = 8
- Tₙ = a + (n − 1)d = −8 + (n − 1) × 8 = 8n − 16
7.For the arithmetic sequence 15, 23, 31, 39, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 7
- d = 23 − 15 = 8
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 8 = 8n + 7
8.Find the 20th term of the arithmetic sequence 16, 23, 30, 37, …
Answer: 149
- a = 16, d = 7
- T20 = 16 + 19 × 7 = 149
9.For the arithmetic sequence 11, 16, 21, 26, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 6
- d = 16 − 11 = 5
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 5 = 5n + 6
10.For the arithmetic sequence −5, −8, −11, −14, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n − 2
- d = −8 − (−5) = −3
- Tₙ = a + (n − 1)d = −5 + (n − 1) × −3 = −3n − 2
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.
Great work. Here's what to try next: